Expected damage

So lets talk about expected damage today. The quick way and the slow way. Then we have the stupid long way around. I will not do that but I know people that do :D Knock your self out ^^

Quick way

So the quick way is really simple. Find out what you will hit on and shorten it down to the amount of attacks you have. Then calculate damage by saying each damage dice is 3,5.

A tangent here but in games I normally count damage dice as a 3. So a normal down swing in damage does not leave me with my pants around my ankles. Same I count my opponents dice at 4 to make sure I do not lose important models to a spike.

Example:
A unit of Mage Hunter Strike Force shoot at a Reckoner. So hitting on sixes and -9 on the damage rolls. Missing on sixes is 10/36. Which is a bit above 1/4. So in a 11 man unit we expect 8 hits. Three dice -9 we expect 1,5 damage per hit. So a MHSF shooting we get about 12 damage.

Slow way

The above version is really good when you are in a game and can't spend the time calculating for real. It does though not take into affect one of the most important principals of damage rolls. Spikes helps damage rolls a lot. Rolling 111 and 666 is the same average as 334 and 443. The triple 6 one does one point more of damage though.

So the correct way to count damage is to add the odds of rolling something and multiply by the damage it does and then add all of it. Then divide by the possible options again.

Example:
A unit of Mage Hunter Strike Force shoot at a reckoner. You hit on a 6 we wait with that. -9 on damage rolls gives us 1/216 of triple 6 doing 9 damage. 3 combinations of 17 dealing 8 damage and so on. The total of this becomes 216 arrows will deal 450 damage. Or about 2.1 damage per arrow. Then we take that times the odds to hit 26/36 we get that each arrow deals approximately. 1,5 damage so 11 MHSF will deal about 16,5 damage. This is really important on 3 dice -10 and upwards rolls. Keep this in mind when facing MHSF.

The 3 dice expected damage looks like this:

-5	-6	-7	-8	-9	-10	-11
5,523148	4,569444	3,662037	2,824074	2,083333	1,458333	0,958333

Example table in case you want to do it for other numbers or other amount of dice:

The roll	Combinations	Damage done	Multiplication
18	1	9	9
17	3	8	24
16	6	7	42
15	10	6	60
14	15	5	75
13	21	4	84
12	25	3	75
11	27	2	54
10	27	1	27
9	25	0	0
8	21	0	0
7	15	0	0
6	10	0	0
5	6	0	0
4	3	0	0
3	1	0	0